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arXiv:1605.03160 · Physical Review A

Decoherence of rotational degrees of freedom

Changchun Zhong, F. Robicheaux

Published Nov 11, 2016• 36 citations
arXivHTMLPDF

Abstract

The mechanism of decoherence for a mesoscopic quantum system with rotational degrees of freedom is studied. From a simple model of elastic scattering, we show that the nondiagonal density-matrix elements of the system exponentially decay. The decay rate depends on the difference of scattering amplitudes for different rotational configurations, leading to the gradual loss of quantum coherence between the pointer states in the orientational space. For a dielectric ellipsoid immersed in a photon-gas environment (assuming no absorption), the decay rate is found to be proportional to the seventh power of the temperature. For an ellipsoidal object interacting with massive particles, the decay rate is proportional to the 5/2 power of the temperature. Both are different from the case of translational decoherence induced by the same environment scattering. For photon scattering, the coherence time in the rotational degrees of freedom is shown to be much shorter than that in the translational degrees of freedom.

DOI
10.1103/physreva.94.052109

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The mechanism of decoherence for a mesoscopic quantum system with rotational degrees of freedom is studied. From a simple model of elastic scattering, we show that the nondiagonal density-matrix elements of the system exponentially decay. The decay rate depends on the difference of scattering amplitudes for different rotational configurations, leading to the gradual loss of quantum coherence between the pointer states in the orientational space. For a dielectric ellipsoid immersed in a photon-gas environment (assuming no absorption), the decay rate is found to be proportional to the seventh power of the temperature. For an ellipsoidal object interacting with massive particles, the decay rate is proportional to the 5/2 power of the temperature. Both are different from the case of translational decoherence induced by the same environment scattering. For photon scattering, the coherence time in the rotational degrees of freedom is shown to be much shorter than that in the translational degrees of freedom.
The use of rotational degrees of freedom of quantum systems in quantum technologies is limited by environmental effects under decoherence mechanism. Here, we study the mechanism of decoherence based on a new formalism of elastic scattering for a nonspherical quantum system prepared in a superposition of rotational degrees of freedom. We show that for a dielectric ellipsoid immersed in an environment composed of thermal photons the rotational decoherence rate depends on the angular differences between the two configurations of the system and the seventh power of the temperature which is different from the translational one. Then we analyze the effect of different values of angular momentum quantum numbers of the environmental spherical harmonics on the rotational decoherence rate.
Motivated by trapping and cooling experiments with nonspherical nanoparticles, we discuss how their combined rotational and translational quantum state is affected by the interaction with a gaseous environment. Based on the quantum master equation in terms of orientation-dependent scattering amplitudes, we evaluate the localization rate for gas collisions off an anisotropic van der Waals--type potential and for photon scattering off an anisotropic dielectric. We also show how pure angular momentum diffusion arises from these open quantum dynamics in the limit of weak anisotropies.
We show how to describe the diffusion of the quantized angular momentum vector of an arbitrarily shaped rigid rotor as induced by its collisional interaction with an environment.We present the general form of the Lindblad-type master equation and relate it to the orientational decoherence of an asymmetric nanoparticle in the limit of small anisotropies.The corresponding diffusion coefficients are derived for gas particles scattering off large molecules and for ambient photons scattering off dielectric particles, using the elastic scattering amplitudes.
We study the effect of the environment on the process of the measurement of a state of a microscopic spin-half system. The measuring apparatus is a heavy particle, whose center-of-mass coordinates can be considered at the end of the measurement as approximately classical, and thus can be used as a pointer. The state of the pointer, which is the result of its interaction with the spin, is transformed into a mixed state by the coupling of the pointer to the environment. The environment is considered to be a gas reservoir, whose particles interact with the pointer. This results in a Fokker-Planck equation for the reduced density matrix of the pointer. The solution of the equation shows that the quantum coherences, which are characteristic to the entangled state between the probabilities to find the pointer in one of two positions, decays exponentially fast in time. We calculate the exponential decay function of this decoherence effect, and express it in terms of the parameters of the model.
Recent advances in levitated optomechanics provide new perspectives for the use of rotational degrees of freedom for the development of quantum technologies as well as for testing fundamental physics. As for the translational case, their use, especially in the quantum regime, is limited by environmental noises, the characterization of which is fundamental in order to assess, control, and minimize their effect, in particular decoherence. Here, we present a general perturbative approach to compute decoherence for a quantum system in a superposition of its rotational degrees of freedom. The specific cases of the dipole-dipole and quadrupole-quadrupole interactions are solved explicitly, and we show that the rotational degrees of freedom decohere on a time scale that can be longer than the translational one.
The phenomenon of decoherence appears when the quantum behaviour of a microsystem is investigated. If the shielding of the considered microsystem from the macroscopic environment is not perfect, typical quantum features, such as the capability to exhibit quantum fringes, are suppressed as an unavoidable result of the interaction with the macroscopic background. Focusing on the centre of mass degrees of freedom of a massive test particle decoherence can typically be described in terms of random momentum transfers with the environment, thus naturally calling for a probabilistic standpoint. In this framework a general connection between the characteristic function of a Lévy process and loss of coherence of a massive quantum system interacting through momentum transfer events with an environment will be put into evidence, relying on Holevo’s characterization of quantum dynamical semigroups in the presence of translational invariance. The relationship with microphysical models and recent experiments on decoherence will also be considered.